I may have found a solution to this problem.
I have the ipod touch 3rd gen (before the Retina display) running 5.1.1, which is the highest iOS version possible (according to itunes). However even after complete wiping and resetting, after logged into App Store I can't download apps that clearly state that they support iOS 5.0 or later. The App icon would appear on the home screen for a quick second, then display "the request action requires the latest version of iOS", then "iOS updates required". I have tried a Canadian Apple ID and a Chinese Apple ID, neither worked. Also, you can't even create new Apple ID on the iPod, will return the same error.
Solution (at least for me): update your itunes on your computer (i did it on a macbook pro, hopefully on Windows it is the same) to the latest version, go to iTunes store and search for the app you want. as long as the App itself states its compatibility with your iOS version, you should be fine. Now download it into itunes. Then plug in the iPod touch and sync the app. You want to be careful about sync options for various content. Pick the manually manage content option and only sycn the App on the App page. I would carefully deselect all sync options about music, video, photo, etc. Otherwise you will wipe out your ipod media content before you know it.
This way, the above mentioned apps, which couldn't be installed locally on the iPod touch, were installed no problem through iTunes. I hope the method works for older iPad as well.
I have to say, although those older iPod touch has smaller screen and less processing power than today's even budget smartphone, they still run pretty smoothly on their highest iOS version. Got to give Apple for that!
